Forward self-similar and discretely self-similar weak solutions of the Navier–Stokes
equations are known to exist globally in time for large self-similar and discretely
self-similar initial data and are known to be regular outside of a space-time
paraboloid. We establish spatial decay rates for such solutions which hold in the
region of regularity provided the initial data has locally subcritical regularity away
from the origin. In particular, we lower the Hölder regularity of the data required to
obtain an optimal decay rate for the nonlinear part of the flow compared to the existing
literature, establish new decay rates without logarithmic corrections for some smooth
data, provide new decay rates for solutions with rough data, and, as an application
of our decay rates, provide new upper bounds on how rapidly potentially nonunique,
discretely self-similar local energy solutions can separate away from the origin.
